^lro*t'     ^(AA^Ctx^el- 


A 


ARITHMETIC  BULLETIN  No.  I. 


Scientific    Measurements    of 

Arithmetical    Abilities    in 

Boston   Public  Schools- 


JANUARY,     1914. 


<^^^— ,    G^tUV^^.^,,^ 


^, 


»y 


Compliments  of  Courtis  Standard   Tests. 


CITY    OF    BOSTON 

PRINTING    DEPARTMENT 

1914 


L6i5"S1 

a  3 


The  following  statistics  are  the  •  results  of  Courtis  Standard 
Tests  applied  in  thirty-five  Boston  Elementary  School  Districts. 
The  tests  were  given  and  the  computations  made  by  senior 
students  of  the  Boston  Normal  School;  the  scoring  was  done 
by  the  regular  class  teachers. 

The  work  was  organized  and  directed  by 

Rose  A.  Carrigan. 


5.-^^ 

.:::^- 


iij 


Total  number  of  districts  tested 35 

Total  number  of  buildings  in  which  tests  were  given     .        .  72 

Total  number  of  classes  tested 525 

Grades  tested: 

IV 119 

V 118 

VI 112 

VII 108 

VIII.    ........  91 

Pre-vocational,  not  classified  ....  3 

Ungraded,  not  classified 2 

Total  number  of  grades  tested 553 

Total  number  of  children  tested 20,646 


TYPES   OF   EXAMPLES   USED   IN   THE  TEST.* 

Addition  (time  allowed,  8  minutes) 572 

253 
948 
529 
936 
223 
358 
»  .  676 
122 


Subtraction  (time  allowed,  4  minutes)  ....     121961783 

90492726 


Multiplication  (time  allowed,  6  minutes),    7942        8736        6837 

72  502  680 


Division  (time  allowed,  8  minutes)        .        .        .        .       49  2  8420 
Series  A,  Test  7,  not  Recorded  in  this  Bulletin. 

*  Courtis  Standard  Tests,  Series  B,  used.     Above  examples  taken  from  Form  1. 

313645 


GRADE  STANDARDS   FOR    1914.  ' 

Tentative  Standards  in  Number  of  Examples  *  Attempted. 


Grades. 


IV. 

V. 

VI. 

VII. 

6 

7 

9 

10 

6 

8 

9 

10 

4 

6 

7 

8 

3 

5 

6 

7 

VIII. 


Test  1,  Attempts 
Test  2,  Attempts 
Test  3,  Attempts 
Test  4,  Attempts 


11 

12 

9 

9 


Established  Standard  in  Number  of  Examples  Right. 
Accuracy  100%  in  all  Tests. 

Note. —  Teachers  are  urged  in  every  case  to  aim  for  100%. 


AVERAGE   MEDIANS  ATTAINED  BY  EACH  GRADE  IN  THE  35  SCHOOL 

DISTRICTS  TESTED. 


Grades. 


IV. 

V. 

VI. 

VII. 

5.8 

7.1 

8.5 

9.6 

2.8 

3.6 

4.7 

5.6 

5.6 

7.5 

9.1 

10.2 

2.7 

4.5 

6.5 

7.3 

4.2 

5.7 

6.9 

8.1 

1.6 

3.3 

4.5 

5.1 

2.9 

4.5 

6.0 

7.3 

.6 

2.1 

3.8 

5.1 

Test  1, 
Test  1, 

Test  2, 
Test  2, 

Test  3, 
Test  3, 

Test  4, 
Test  4, 


Attempts . 
Rights 


Attempts . 
Rights 


Attempts . 
Rights 


Attempts . 
Rights 


11.2 
7.3 

11.6 

8.7 

9.4 
6.6 

9.0 
7.1 


♦  In  all  the  testing  work  the  word  "Attempts  "  is  used  to  mean  complete  answers.    A  partial  answer 
is  not  counted  as  an  example  attempted. 


Ranges  in  the  Class  Medians  f  Attained  in  Each  Grade. 


Grades. 


IV. 


V. 


VI. 


VII. 


VIII. 


Test  1,  Attempts. 
Test  1,  Rights. .  . 


Test  2,  Attempts . 
Test  2,  Rights.  .  . 


Test  3,  Attempts . 
Tests,  Rights.  .  . 


Test  4,  Attempts . 
Test  4,  Rights.  .  . 


*  3.6—  8.7 
.8—  7.0 

3.7—10.8 
.5—  6.5 

1.6—  6.5 
.5—  3.8 

.5—  6.0 
.5—  2.5 


4.0—10.4 
1.3—  7.0 

3.8—10.3 
1.2—  8.2 

3.7—  8.4 
.7—  5.4 

1.9—  9.6 
.5—  4.8 


3.4—15.0 
.5—11.0 

5.0—12.3 
3.0—10.3 

4.9—  9.5 
2.0—  7.5 

2.5—  9.7 
.8—  7.3 


3.5—14.2 
1.4—11.0 

6.0—16.0 
3.8—14.3 

5.0—12.9 
1.9—  9.2 

4.2—10.5 
1.7—  9.0 


5.7—19.0 
4.0—11.4 

5.5—21.8 
3.0—17.3 

7.0—15.5 
2.3—10.8 

3.6—15.0 
1.6—12.7 


*  This  means  that  the  lowest  class  median  in  all  the  fourth  grades  tested  was  3.6,  while  the  highest 
class  median  in  all  the  fourth  grades  tested  reached  8.7.  Notice  the  wide  difference  in  median  ability 
shown  in  the  respective  classes  of  each  grade,  for  example,  addition  in  the  eighth  grade. 

t  The  median  is  the  mid  point  of  class  achievement.  Above  it  and  below  it  are  an  equal  number  of 
individual  scores. 


Ranges  in  the  Per  Cents  of  *  Variability. 


Grades. 


IV. 


V. 


VI. 


VII. 


VIII. 


Test  1,  Attempts. 
Test  1,  Rights..., 


Test  2,  Attempts. 
Test  2,  Rights. . . , 


Test  3,  Attempts . 
Tests,  Rights..., 


Test  4,  Attempts . 
Test  4,  Rights... 


11—  47 
10—100 

17—100 
18—100 

24—100 
13—100 

26—100 
13—100 


15—100 
24—100 

12—100 
12—100 

16—100 
12—100 

19—100 
13—100 


12—  41 
18—100 

9—  64 
16—  96 

11—  49 
17—100 

18—100 
16—100 


10—40 
22—79 

10—38 
15—75 

10—43 
17—91 

12—84 
13—95 


10—37 
14—67 

8—43 

18—78 

10—46 
18—75 

12—57 
15—74 


*  Not  more  than  10%  of  variability  in  a  class  is  considered  desirable  in  this  work  on  fundamentals. 
Defective  children  should  be  segregated.  Individuals  among  normal  children  should  be  helped,  when 
necessary,  to  overcome  specific  difficulties  and  all  pupils  should  be  led  to  feel  responsible  for  bringing 
their  own  work  up  to  the  standards  set  for  their  grade. 


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